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Add some notes to micro magnesium study channel die setup.

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JMBBM13b/README.md
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# Computational micromechanics of bioabsorbable magnesium stents
Journal Article: https://doi.org/10.1016/j.jmbbm.2014.01.007
Supporting Data - including original software versions: https://zenodo.org/records/11184080
If you don't have access to the paper the content is very similar to that in my thesis section 5.4, available for download at: https://researchrepository.universityofgalway.ie/entities/publication/6168a11d-5962-4e52-97d1-6f2684a97ac2
The UMAT `UCrys_HCP_Only.for` is used for the simulations in the paper.
# Running simulations
The channel die experiments use `CDIE_1E.inp` as in input file. In that file the following material is specified:
## Abaqus User Material ##
The Abaqus UMAT `UCrys_HCP_Only.for` is used for the simulations in the paper.
In the UMAT we assume a cartesian `GLOBAL` axis for the overall problem and a cartesian `LOCAL` axis to define the orientation of the crystal. Via input properties (`PROPS`) 3-5 and 6-8 we specify the directions of the `LOCAL` x and y axes in the `GLOBAL` coordinate system, assuming an orthogonal `LOCAL` z axis given by the cross-product with 'right hand rule'.
A sample input file `MATERIAL` specification is shown for the UMAT:
```
*MATERIAL, NAME=MATERIAL-1
@ -19,7 +28,7 @@ The channel die experiments use `CDIE_1E.inp` as in input file. In that file the
*
```
which sets the 22 input properties used in the UMAT. The propeties are as follows:
which sets the 22 input properties. These propeties are as follows:
``` fortran
c PROPS
@ -47,14 +56,23 @@ c 21) Twin system hardening param
c 22) Twin system hardening param
c
```
We assume a cartesian GLOBAL axis for the overall multi-component problem and a cartesian LOCAL axis to define the orientation of the crystal. Via input properties (PROPS) 3-5 and 6-8 we specify the directions of the LOCAL x and y axes in the GLOBAL coordinate system, assuming an orthonal LOCAL z axis given by the cross-product with 'right hand rule'.
In the paper, channel die simulation loading and constraint directions are described via Miller-Bravais indices, which are (informally) a way to describe directions in the crystal lattice, and can be regarded as the inverted intersection coordinates of planes described in crystal specific coordinate systems.
## Channel Die Simulations ##
For the HCP material here four axes are used, three (a_1, a_2, a_3) are on one of the crystal basal planes with equal angles between them (120 degrees) and the fourth (c) is normal to the basal plane. Thus we have three coordinate systems in total, the HCP lattice system via MB indices, the cartesian crystal local LOCAL system and the GLOBAL system.
The channel die simulations described in the paper use `CDIE_1E.inp` as an input file.
![Channel Die Simulation Schematic](ChannelDie.png)
Loading and constraint directions are described via [Miller-Bravais](https://en.wikipedia.org/wiki/Miller_index) indices, which are (informally) a way to describe directions in the crystal lattice, and can be regarded as the inverted intersection coordinates of planes described in crystal-specific coordinate systems.
For the HCP material here four axes are used, three (`a_1`, `a_2`, `a_3`) are on one of the crystal basal planes with equal angles between them (120 degrees) and the fourth (`c`) is normal to the basal plane. Thus we have three coordinate systems in total:
* the HCP lattice system via MB indices
* the cartesian crystal local `LOCAL` system
* the `GLOBAL` system.
In the simulated experiment the die is closed in the GLOBAL (negative) z direction via boundary condition.
In the simulated experiment the die is always closed in the `GLOBAL` (negative) z direction via this boundary condition in the INP file:
```
** Name: BC-4 Type: Displacement/Rotation
@ -62,9 +80,23 @@ In the simulated experiment the die is closed in the GLOBAL (negative) z directi
Set-2, 1, 1, -1.
```
Another direction allows the the material to freely deform (GLOBAL x or y, not sure which).
while another direction allows the the material to freely deform (`GLOBAL` x or y, not sure which).
To determine the suitable crystal input orientation parameters for each test it is necessary to find suitable coordinates for the LOCAL crystal axes in the GLOBAL system via the defined Miller indices.
To replicate the series of channel die simulations, with loading and constraint directions shown in the table below:
| Simulation | Load Direction | Constraint Direction |
| --- | --- | --- |
| A | `[0001]` | `[101^0]` |
| B | `[0001]` | `[12^10]` |
| C | `[101^0]` | `[0001]` |
| D | `[12^10]` | `[0001]` |
| E | `[101^0]` | `[12^10]` |
| F | `[12^10]` | `[101^1]` |
we thus need to determine suitable crystal input orientation parameters for each test, so that the crystal is loaded and constrainted accoring to the described Miller-Bravais indices.
### Determing UMAT properties for crystal orientation ###
Taking the first case as an example, load direction `[0 0 0 1]` means the loading will happen along the `c` axis of the crystal (or perpendicular to the basal plane). This contrains the crystal local `x` and `y` axes to be normal to the global `z` direction `(0, 0, 1)`.